Business Cal


The spot price of crude oil during the period 2000-2005 can be approximated byP(t) = 5t + 25 dollars per barrel(0 ≤ t ≤ 5) in year t, where t = 0 represents 2000. Saudi Arabia’s crude oil production over the same period can be approximated byQ(t) = 0.082t2 − 0.22t + 8.2 million barrels per day†(0 ≤ t ≤ 5) Use these models to estimate Saudi Arabia’s daily oil revenue and also its rate of change in 2005. (Round your answers to the nearest $1 million.)daily oil revenue$  457.5million rate of change in 2005$   million/yr FIND RATE change in 2005Calculate the derivative of the function. HINT [See Example 1.]f(x) = (6.4x − 6)−2 + (4.3x − 4)−2f ‘(x) =                                        The percentage y (of total personal consumption) an individual spends on food is approximatelyy = 35x−0.25 percentage points  (6.5 ≤ x ≤ 17.5) where x is the percentage the individual spends on education.† An individual finds that she is spendingx = 7 + 0.2tpercent of her personal consumption on education, where t is time in months since January 1. Use direct substitution to express the percentage y as a function of time t (do not simplify the expression). (NOTE: January 1 is represented by t = 0.)y(t) =                                         Use the chain rule to estimate how fast the percentage she spends on food is changing on August 1. (Round your answer to two decimal places.)Answer:Specify the units.

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